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1
In saucepan over medium heat, gently reduce apple cider to about 1/4 cup by simmering for 20-30 minutes. Set aside to cool. In large bowl, whisk together flour, baking powder, baking soda, cinnamon, salt, and nutmeg. Set aside.
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2
Add butter and sugar to stand mixer fitted with paddle attachment. Cream on medium speed until the mixture is smooth and fluffy, about 3 minutes. Add eggs, 1 at a time, continuing to mix until eggs are completely incorporated. Reduce speed to low and gradually drizzle in reduced apple cider and buttermilk, mixing just until combined, about 1 minute. Add flour mixture and continue to mix until the dough comes together. Do not overmix.
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3
Line two rimmed baking sheets with parchment paper and sprinkle generously with flour. Turn dough onto one sheet and sprinkle the top with flour. Flatten dough to even 1/2-inch thickness with hands or rolling pin, sprinkling with flour as necessary.
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4
Transfer dough to the freezer until slightly hardened, about 20 minutes. Using 3-inch doughnut cutter, cut out doughnut shapes and donut holes. Place cut doughnuts and doughnut holes onto second sheet pan. Refrigerate doughnuts for 20 to 30 minutes. (You can re-roll scraps of dough, refrigerate them briefly and cut additional doughnuts from dough.)
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5
Add enough oil or shortening to Dutch oven or wok to measure depth of about 3 inches. Attach candy thermometer to side of the pan and heat over medium heat until oil reaches 350 degrees. Line large plate with several layers of paper towels.
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6
Carefully add doughnuts to oil a few at a time, being careful not to crowd pan. Fry until golden brown, about 60 seconds. Turn doughnuts over and fry until second side is golden, 30 to 60 seconds longer.
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7
Drain fried donuts on paper towels. Dip top of the warm doughnuts in cinnamon sugar and serve immediately.
